Invariants of derived equivalences for admissible fractional Brauer graph algebras

TL;DR

This paper investigates invariants of derived equivalences for a new subclass of self-injective algebras called admissible fractional Brauer graph algebras, linking them to gentle algebras.

Contribution

It introduces combinatorial invariants for derived equivalences and shows these algebras are related to gentle algebras via repetitive and trivial extension constructions.

Findings

Provided combinatorial invariants for derived equivalences.

Showed these algebras are repetitive and $r$-fold trivial extensions of gentle algebras.

Characterized derived equivalences within this algebra subclass.

Abstract

Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial algebras, and provide several easily checkable combinatorial invariants for derived equivalences between them. In particular, we show that these algebras can be viewed as repetitive algebras and $r$-fold trivial extensions of gentle algebras.